The study of the propagation of seismic waves has often been described the properties and structure of the Earth’s interior. Many problems in applied mathematics and theoretical seismology can be solved as boundary value problems by representing the Earth as a layered medium with the certain thickness and mechanical properties. Seismology is a science based on DATA called seismograms which are records of mechanical vibration of the Earth. here are two types of waves, generated by earthquakes body waves and surface waves. Body waves are faster than surface waves, and then these are well observed by the seismometer. But the study of surface wave from direct seismic DATA is not so easy to investigate. In those cases, mathematical studies play an essential role to examine these kinds of waves. The importance of surface wave is that the surface wave carries a significant amount of energy from shallow shocks due to the presence of non-homogeneity, anisotropy and various initial stresses in the Earth layered media.In this study, we represent a mathematical modelling of seismic surface wave propagation in different Earth layered media with suitable boundary conditions. The work deals with the propagation of Love wave and Rayleigh (surface waves) at the surface of a highly anisotropy non-homogeneous semi-infinite medium. Later on, we have extended our study for multilayered media. The analytical and numerical approaches are taken over to investigate the phase velocity and group velocity of Love and Rayleigh waves in a layer of composite structures. The mathematical analysis of the problem has deal with the technique of separation of variables and Whittaker function to solve the problem analytically and finite difference method to solve numerically. This study aims to establish the stability of phase velocity and group velocity (in a unit disk) and the effect of non-homogeneity, anisotropy, corrugation and initial stress on the dispersion of Love wave and Rayleigh wave.Keywords: Surface wave, Non-homogeneous, Anisotropy, Phase velocity, Group velocity

Short-Bio:

Dr. Manna was born in a village of South 24 Parganas, West Bengal on November 02nd 1987. He did his B.Sc. in Mathematics Honours from the University of Calcutta. He had obtained his Master degree in Mathematics Computing from Indian School of Mines Dhanbad in 2011. He was awarded the Ph. D. degree in Applied Mathematics from Indian Institute of Technology (ISM) Dhanbad in 2015. After his Ph.D., Dr. Manna worked as a Post-Doctoral Research Scientist in Indian Institute of Science Education and Research Kolkata. He has been awarded for “National Post-Doctoral Fellowship” from SERB, Department of Science & Technology, Government of India in 2016. He also has been awarded for “Dr. D.S. Kothari Post Doctoral Fellowship” from University Grants Commission, Government of India in 2016. Presently, he is working as a Faculty (Assistant Professor level) in the Discipline of Mathematics, IIT Indore.